the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 May 2023
Clustering of settling microswimmers in turbulence
Abstract. Clustering of plankton plays a vital role in several biological activities including feeding, predation and mating. Gyrotaxis is one of the mechanisms that induces clustering. A recent study reported a fluid inertial torque acting on a spherical micro-swimmer, which is analogous to a gyrotactic torque. In this study, we model plankton cells as micro-swimmers that are subject to gravitational sedimentation as well as a fluid inertial torque. We use direct numerical simulations to obtain the trajectories of swimmers in homogeneous isotropic turbulence, and investigate their clustering by Voronoï analysis. Our findings indicate that fluid inertial torque leads to notable clustering, with its intensity depending on the swimming and settling speeds of swimmers. By Voronoï analysis, we demonstrate that swimmers preferentially sample downwelling regions where clustering is more prevalent.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2023-911', Anonymous Referee #1, 16 Aug 2023
This paper discusses the statistical properties of settling microswimmers in turbulence. In the first part the mathematical
model for settling swimmers is derived and in the second part the results of numerical simulations in a turbulent flow are
discussed.I am not convinced that the present version of the manuscript deserves publication.
The derivation of the model (section 2.1) is interesting and its study probably deserves publication. The main objection I
have is that in the limit discussed in this paper (eqs. 5-8) the model is identical to the Kessler model for gyrotaxis which
has been already studied in the same flow and with the same statistical approach (clustering in terms of Voronoi distribution
and preferential concentration). Therefore, it is not clear what are the new results of this manuscript.Moreover, this is not clearly discussed in the paper. After eqs. (5-8), it is written that "the second term on the rhs of (8)
is analogous to the gyrotactic effect", while the model (6,8) is identical to the standard gyrotactic model.In conclusion, I think that it would be interesting to investigate the model general model (3,4) and compare it with the known gyrotactic limit.
This would add something new to our understanding to swimming microorganisms in turbulence.
Moreover, my impression is that, with the typical values discussed after (9), the range of the Stokes numbers is comparable with the other
dimensionless parameters and therefore the limit St->0 is not justified.Minor point: the presentation of the model and the results is not always clear. For example, the settling speed v_g is not defined.
Citation: https://doi.org/10.5194/egusphere-2023-911-RC1 - AC1: 'Reply on RC1', Jingran Qiu, 11 Oct 2023
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RC2: 'Comment on egusphere-2023-911', Anonymous Referee #2, 02 Sep 2023
This paper discusses clustering of microswimmers in homogeneous isotropic turbulence. The effects that lead to clustering are negative buoyancy and a fluid inertial torque (taken from Candelier et al. 2022) that effectively introduces gyrotactic behaviour.
As the authors point out, there have been a number of papers examining clustering of microswimmers due to gyrotaxis in homogeneous isotropic turbulence over the past one or two decades.
The main contribution of the present paper appears to be the addition of the inertial torque (second term on the RHS of Eq. 2) to an otherwise standard model of a microswimmer that has previously been studied. This inertial torque comes from the work of Candelier et al. (2022). Candelier et al. go to great lengths to describe the various orders of approximations in their work and the conditions under which their results are valid. However, the authors of the present paper do not clarify whether the situation they consider is consistent with including this extra term and whether they can include only this extra term without the need to include other extra terms for consistency. In a similar vein, the authors (between Eq 4 and Eq 5) state the microswimmer inertia is negligible and consider the limit where their St —> 0 without any explanation of whether the limit exits at finite Re (required for the inertial torque to be relevant).
The final microswimmer equations used in the simulations (Eq 5 — Eq 8) are dubious for the reasons outlined above. However, taken them as a given, the results are not particularly novel because these microswimmer equations simplify to those investigated before (spherical gyrotactic settling microswimmers) and thus the results are not particularly novel. Additionally, the authors apply their model to extremely high swimming speeds and high settling speeds (L91) without any comment on whether this range of values are consistent with their assumptions. (I suspect they are not).
Minor comments:
L16, ‘accumulates’ — check grammar
L17, ‘clustering’ — check grammar
L22, ‘the inverse of a timescale B’ — unclear writing. It needs to be explained here what B is (timescale for reorientation against gravity in an otherwise quiescent environment).
Eq. 4 — v_s\prime should be \Phi_s
L146, ‘variance of Voronoi volumes’ — I’m not sure whether the authors mean the location of the peak of the distribution or indeed the variance.Citation: https://doi.org/10.5194/egusphere-2023-911-RC2 - AC2: 'Reply on RC2', Jingran Qiu, 11 Oct 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-911', Anonymous Referee #1, 16 Aug 2023
This paper discusses the statistical properties of settling microswimmers in turbulence. In the first part the mathematical
model for settling swimmers is derived and in the second part the results of numerical simulations in a turbulent flow are
discussed.I am not convinced that the present version of the manuscript deserves publication.
The derivation of the model (section 2.1) is interesting and its study probably deserves publication. The main objection I
have is that in the limit discussed in this paper (eqs. 5-8) the model is identical to the Kessler model for gyrotaxis which
has been already studied in the same flow and with the same statistical approach (clustering in terms of Voronoi distribution
and preferential concentration). Therefore, it is not clear what are the new results of this manuscript.Moreover, this is not clearly discussed in the paper. After eqs. (5-8), it is written that "the second term on the rhs of (8)
is analogous to the gyrotactic effect", while the model (6,8) is identical to the standard gyrotactic model.In conclusion, I think that it would be interesting to investigate the model general model (3,4) and compare it with the known gyrotactic limit.
This would add something new to our understanding to swimming microorganisms in turbulence.
Moreover, my impression is that, with the typical values discussed after (9), the range of the Stokes numbers is comparable with the other
dimensionless parameters and therefore the limit St->0 is not justified.Minor point: the presentation of the model and the results is not always clear. For example, the settling speed v_g is not defined.
Citation: https://doi.org/10.5194/egusphere-2023-911-RC1 - AC1: 'Reply on RC1', Jingran Qiu, 11 Oct 2023
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RC2: 'Comment on egusphere-2023-911', Anonymous Referee #2, 02 Sep 2023
This paper discusses clustering of microswimmers in homogeneous isotropic turbulence. The effects that lead to clustering are negative buoyancy and a fluid inertial torque (taken from Candelier et al. 2022) that effectively introduces gyrotactic behaviour.
As the authors point out, there have been a number of papers examining clustering of microswimmers due to gyrotaxis in homogeneous isotropic turbulence over the past one or two decades.
The main contribution of the present paper appears to be the addition of the inertial torque (second term on the RHS of Eq. 2) to an otherwise standard model of a microswimmer that has previously been studied. This inertial torque comes from the work of Candelier et al. (2022). Candelier et al. go to great lengths to describe the various orders of approximations in their work and the conditions under which their results are valid. However, the authors of the present paper do not clarify whether the situation they consider is consistent with including this extra term and whether they can include only this extra term without the need to include other extra terms for consistency. In a similar vein, the authors (between Eq 4 and Eq 5) state the microswimmer inertia is negligible and consider the limit where their St —> 0 without any explanation of whether the limit exits at finite Re (required for the inertial torque to be relevant).
The final microswimmer equations used in the simulations (Eq 5 — Eq 8) are dubious for the reasons outlined above. However, taken them as a given, the results are not particularly novel because these microswimmer equations simplify to those investigated before (spherical gyrotactic settling microswimmers) and thus the results are not particularly novel. Additionally, the authors apply their model to extremely high swimming speeds and high settling speeds (L91) without any comment on whether this range of values are consistent with their assumptions. (I suspect they are not).
Minor comments:
L16, ‘accumulates’ — check grammar
L17, ‘clustering’ — check grammar
L22, ‘the inverse of a timescale B’ — unclear writing. It needs to be explained here what B is (timescale for reorientation against gravity in an otherwise quiescent environment).
Eq. 4 — v_s\prime should be \Phi_s
L146, ‘variance of Voronoi volumes’ — I’m not sure whether the authors mean the location of the peak of the distribution or indeed the variance.Citation: https://doi.org/10.5194/egusphere-2023-911-RC2 - AC2: 'Reply on RC2', Jingran Qiu, 11 Oct 2023
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Jingran Qiu
Zhiwen Cui
Eric Climent
Lihao Zhao
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1027 KB) - Metadata XML